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This mock test of Central Forces MCQ Level – 2 for IIT JAM helps you for every IIT JAM entrance exam.
This contains 10 Multiple Choice Questions for IIT JAM Central Forces MCQ Level – 2 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The gravitational potential of two homogeneous spherical shells *A* and *B* of same surface density at their respective centres are in the ratio **3 : 4**. If the two shells coalesce into single one such that surface density remains same, then the ratio of potential at an internal point of the new shell of shell *A* is equal to :

Solution:

where σ is surface density

for New shell of mass *M* and radius *R*.

The correct answer is: **5 : 3**

QUESTION: 2

A satellite is launched in the equatorial plane in such a way that it can transmit signals upto 60° latitude on the earth. The angular velocity of the satellite is :

Solution:

In (where *OR* is orbital radius)

Here gravitational force will provide the required centripetal force.

The correct answer is:

QUESTION: 3

A cavity of radius * R/2* is made inside a solid sphere of radius

**[**Here, **g****=** **GM/R**^{2}, where * M* is the mass of the sphere without cavity

Solution:

Gravitational field at mass '*m*' due to full solid sphere

Gravitational field at mass '*m*' due to cavity (-ρ)

Net gravitational field

Net force on * m* →

The correct answer is:

QUESTION: 4

A tunnel is dug along the diameter of the earth (Radius * R* and mass

Solution:

Let the minimum speed imparted to the particle of mass * m* so that it just reaches surface of earth is

Solving we get

The correct answer is:

QUESTION: 5

Maximum height reached by a rocket fired with a speed equal to 50% of the escape velocity from earth’s surface is :

Solution:

Applying energy conservation

The correct answer is: **R/3**

QUESTION: 6

The percentage change in the acceleration of the earth towards the sun from a total eclipse of the sun to the point where the moon is on a side of earth directly opposite to the sun is :

Solution:

During total eclipse-

Total attraction due to sun and moon.

When moon goes on the opposite side of earth.

Effective force of attraction,

Change in force,

Change in acceleration of earth

Average force on earth,

Average acceleration of earth,

%age change in acceleration

The correct answer is:

QUESTION: 7

A small area is removed from a uniform spherical shell of mass * M* and radius

Solution:

The Gravitational field at the centre of the hole due to the remaining mass is

QUESTION: 8

A point *P* lies on the axis of a fixed ring of mass * M* and radius

Solution:

Gravitational potential at ‘*P*’

Gravitational potential at ‘*O*’

work energy theorem

The correct answer is:

QUESTION: 9

Two particles of combined mass * M*, placed in space with certain separation, are released. Interaction between the particles is only of gravitational nature and there is no external force present. Acceleration of one particle with respect to the other when separation between them is

Solution:

acceleration of *M*_{1} w.r.t. *M*_{2
}

The correct answer is:

QUESTION: 10

Four similar particles of mass * m* are orbiting in a circle of radius

Solution:

Centripetal force = net gravitational force

The correct answer is:

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